Answer:
The equation of line is y = 3 x - 1 , i.e option A .
The rate of change = m = 3
Step-by-step explanation:
Given as :
The points are
([tex]x_1[/tex],[tex]y_1[/tex] ) = (- 2, -7)
([tex]x_2[/tex],[tex]y_2[/tex] ) = (1 , 2)
Let The slope = m
Now, The slope is calculated in points form
So, Slope = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
I.e m = [tex]\dfrac{2-(-7)}{1-(-2)}[/tex]
or, m = [tex]\dfrac{9}{3}[/tex]
I.e m = 3
So, The slope of points = m = 3
I,e Rate of change = m = 3
Now, the equation of line in slope - point form can be written as
y -[tex]y_1[/tex] = m ( x - [tex]x_1[/tex])
where m is the slope of line
i.e y - (-7) = ( 3 ) × ( x - (-2) )
or, y + 7 = 3 × (x + 2)
∴ y + 7 = 3 x + 6
Or, y = 3 x + 6 - 7
Or, y = 3 x - 1
So, The equation of line is y = 3 x - 1
Hence, The equation of line is y = 3 x - 1 , i.e option A .
And The rate of change = m = 3 Answer
